The low-energy bands of non-interacting electrons for \(N=16\)  layers with a Bernal stacking fault at the center \(n=m=8\)  are shown in Fig. REF (a).
For \(m,n \gg 1\) , the non-interacting low-energy bands behave almost as if they arise from two disconnected pieces of RMG with \(m\)  and \(n\)  layers, respectively. This may be understood by deriving an effective low-energy four band Hamiltonian, following the procedure described previously for bilayer graphene [1]}, [2]}, in a basis of orbitals on \(A_1\) , \(B_m\) , \(A_{m+1}\) , \(B_N\)  sites. For \(k \ll k_c\)  and \(E \ll \gamma _1\) , we find
\(H_{\mathrm {Bernal}}^{(m,n)} = \gamma _1\left(\begin{array}{cccc}0 & - (-\kappa ^{\dagger })^m & 0 & (-\kappa ^{\dagger })^{m+n-2} \\- (-\kappa )^m & 0 & - c_{mn} (k/k_{\mathrm {c}})^{2(\ell -1)}\kappa ^2 & 0 \\0 & - c_{mn} (k/k_{\mathrm {c}})^{2(\ell -1)}(\kappa ^{\dagger })^2 & 0 & - (-\kappa ^{\dagger })^n \\(-\kappa )^{m+n-2} & 0 & - (-\kappa )^n & 0 \\\end{array}\right) , \) 
